Question: Reduce to lowest terms: $ \dfrac{6}{7} \div - \dfrac{6}{5} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{6}{5}$ is $- \dfrac{5}{6}$ Therefore: $ \dfrac{6}{7} \div - \dfrac{6}{5} = \dfrac{6}{7} \times - \dfrac{5}{6} $ $ \phantom{ \dfrac{6}{7} \times - \dfrac{5}{6}} = \dfrac{6 \times -5}{7 \times 6} $ $ \phantom{ \dfrac{6}{7} \times - \dfrac{5}{6}} = \dfrac{-30}{42} $ The numerator and denominator have a common divisor of $6$, so we can simplify: $ \dfrac{-30}{42} = \dfrac{-30 \div 6}{42 \div 6} = -\dfrac{5}{7} $